The present invention generally relates to measuring optical errors of optical systems. More particularly, the invention relates to improved methods and systems for reconstructing a wavefront surface/elevation map of optical tissues of an eye and to improved systems for calculating an ablation pattern.
Known laser eye surgery procedures generally employ an ultraviolet or infrared laser to remove a microscopic layer of stromal tissue from the cornea of the eye. The laser typically removes a selected shape of the corneal tissue, often to correct refractive errors of the eye. Ultraviolet laser ablation results in photodecomposition of the corneal tissue, but generally does not cause significant thermal damage to adjacent and underlying tissues of the eye. The irradiated molecules are broken into smaller volatile fragments photochemically, directly breaking the intermolecular bonds.
Laser ablation procedures can remove the targeted stroma of the cornea to change the cornea's contour for varying purposes, such as for correcting myopia, hyperopia, astigmatism, and the like. Control over the distribution of ablation energy across the cornea may be provided by a variety of systems and methods, including the use of ablatable masks, fixed and moveable apertures, controlled scanning systems, eye movement tracking mechanisms, and the like. In known systems, the laser beam often comprises a series of discrete pulses of laser light energy, with the total shape and amount of tissue removed being determined by the shape, size, location, and/or number of laser energy pulses impinging on the cornea. A variety of algorithms may be used to calculate the pattern of laser pulses used to reshape the cornea so as to correct a refractive error of the eye. Known systems make use of a variety of forms of lasers and/or laser energy to effect the correction, including infrared lasers, ultraviolet lasers, femtosecond lasers, wavelength multiplied solid-state lasers, and the like. Alternative vision correction techniques make use of radial incisions in the cornea, intraocular lenses, removable corneal support structures, and the like.
Known corneal correction treatment methods have generally been successful in correcting standard vision errors, such as myopia, hyperopia, astigmatism, and the like. However, as with all successes, still further improvements would be desirable. Toward that end, wavefront measurement systems are now available to accurately measure the refractive characteristics of a particular patient's eye. One exemplary wavefront technology system is the VISX WaveScan® System, which uses a Hartmann-Shack wavefront lenslet array that can quantify aberrations throughout the entire optical system of the patient's eye, including first- and second-order sphero-cylindrical errors, coma, and third and fourth-order aberrations related to coma, astigmatism, and spherical aberrations.
Wavefront measurement of the eye may be used to create a high order aberration map or wavefront elevation map that permits assessment of aberrations throughout the optical pathway of the eye, e.g., both internal aberrations and aberrations on the corneal surface. The aberration map may then be used to compute a custom ablation pattern for allowing a surgical laser system to correct the complex aberrations in and on the patient's eye. Known methods for calculation of a customized ablation pattern using wavefront sensor data generally involves mathematically modeling an optical surface of the eye using expansion series techniques. More specifically, Zernike polynomials have been employed to model the optical surface, as proposed by Liang et al., in Objective Measurement of Wave Aberrations of the Human Eye with the Use of a Harman-Shack Wave-front Sensor, Journal Optical Society of America, Jul. 1994, vol. 11, No. 7, pp. 1–9, the entire contents of which is hereby incorporated by reference. Coefficients of the Zernike polynomials are derived through known fitting techniques, and the refractive correction procedure is then determined using the shape of the optical surface of the eye, as indicated by the mathematical series expansion model.
The Zernike function method of surface reconstruction and its accuracy for normal eyes have been studied extensively for regular corneal shapes. See Schweigerling, J., and Grievenkamp, J. E., “Using corneal height maps and polynomial decomposition to determine corneal aberrations, ” Opt. Vis. Sci., Vol. 74, No. 11 (1997) and Gurao, A. and Artal, P., “Corneal wave aberration from videokeratography: Accuracy and limitations of the procedure,” JOSAA, Vol. 17, No. 6 (2000). Some commentators have shown that the 6th order Zernike polynomial reconstruction method provide an inferior fit when compared to a method of Bhatia-Wolf polynomials. See D. R. Ishkander et al., “An Alternative Polynomial Representation of the Wavefront Error Function,” IEEE Transations on Biomedical Engineering, Vol. 49, No. 4, (2002). The discrepancy was most significant for eyes with a keratoconus condition. It has further been suggested that the known Zernike polynomial modeling methods may result in errors or “noise” which can lead to a less than ideal refractive correction. Furthermore, the known surface modeling techniques are somewhat indirect, and may lead to unnecessary errors in calculation, as well as a lack of understanding of the physical correction to be performed.
Therefore, in light of above, it would be desirable to provide improved methods and systems for mathematically modeling optical tissues of an eye.